Fraction Action: Solving Equations with Fractional Coefficients

Mathematics Grades 6th Grade 3:28 Video
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Lesson Description

Learn two cool ways to solve equations when fractions are mixed in! This lesson uses a video to guide you through multiplying by the denominator and using reciprocals to find the value of the variable.

Video Resource

Solving Equations with Fractional Coefficients | Expressions & Equations | Grade 6

Math is Simple!

Duration: 3:28
Watch on YouTube

Key Concepts

  • Solving equations
  • Fractional coefficients
  • Reciprocal of a fraction
  • Inverse operations

Learning Objectives

  • Students will be able to solve equations with fractional coefficients by multiplying both sides by the denominator.
  • Students will be able to solve equations with fractional coefficients by multiplying both sides by the reciprocal of the fraction.
  • Students will be able to explain the relationship between multiplication and division as inverse operations.

Educator Instructions

  • Introduction (5 mins)
    Begin by asking students what they already know about solving equations. Review the concept of a variable and a coefficient. Briefly discuss what a fraction represents. Then, introduce the video.
  • Video Viewing (7 mins)
    Play the video "Solving Equations with Fractional Coefficients | Expressions & Equations | Grade 6" from Math is Simple! Encourage students to take notes on the two methods presented.
  • Guided Practice (15 mins)
    Work through example problems on the board, demonstrating both methods from the video. Encourage student participation by asking questions and having them help solve the problems. Start with simpler fractions and gradually increase the difficulty.
  • Independent Practice (15 mins)
    Assign students practice problems to solve independently. Circulate the classroom to provide assistance as needed. Offer both types of problems, one where multiplying by the denominator is easier, and another where the reciprocal method is easier.
  • Wrap-up and Assessment (8 mins)
    Review the key concepts and answer any remaining questions. Administer the multiple-choice and fill-in-the-blank quizzes to assess student understanding.

Interactive Exercises

  • Fraction Equation Challenge
    Divide the class into teams and present them with challenging equations with fractional coefficients. The first team to correctly solve the equation wins a point. Vary the complexity of the fractions to keep students engaged.
  • Whiteboard Races
    Give each student a whiteboard and a marker. Call out an equation and have students solve it on their whiteboards. Check answers quickly and provide feedback.

Discussion Questions

  • Which method for solving equations with fractional coefficients do you prefer and why?
  • Can you think of a real-world scenario where you might need to solve an equation with a fractional coefficient?
  • What are some common mistakes people make when solving equations with fractions, and how can you avoid them?

Skills Developed

  • Problem-solving
  • Algebraic reasoning
  • Working with fractions
  • Applying inverse operations

Multiple Choice Questions

Question 1:

What is the first step in solving the equation (1/2)x = 5 using the denominator method?

Correct Answer: Multiply both sides by 2

Question 2:

What is the reciprocal of 3/4?

Correct Answer: 4/3

Question 3:

If (2/5)x = 8, what is the value of x?

Correct Answer: 20

Question 4:

When solving an equation, what does 'doing the inverse operation' mean?

Correct Answer: Doing the opposite operation

Question 5:

What is a coefficient?

Correct Answer: A number multiplied by a variable

Question 6:

Which operation is the inverse of multiplication?

Correct Answer: Division

Question 7:

Why do we multiply both sides of an equation by the same number?

Correct Answer: To keep the equation balanced

Question 8:

Solve for x: (1/3)x = 7

Correct Answer: 21

Question 9:

When using the reciprocal method, what do you multiply the fractional coefficient by?

Correct Answer: The reciprocal of the fraction

Question 10:

In the equation (3/5)x = 15, what is the coefficient?

Correct Answer: 3/5

Fill in the Blank Questions

Question 1:

To solve an equation with a fractional coefficient, you can multiply both sides by the ____________ of the fraction.

Correct Answer: reciprocal

Question 2:

The number attached to the variable by multiplication is called the ____________.

Correct Answer: coefficient

Question 3:

When solving an equation, it is important to keep both sides ____________.

Correct Answer: balanced

Question 4:

The inverse operation of multiplication is ____________.

Correct Answer: division

Question 5:

If (1/4)x = 6, then x = ____________.

Correct Answer: 24

Question 6:

Multiplying by the denominator gets rid of the ____________ in the equation.

Correct Answer: fraction

Question 7:

Another way to solve equations with fractional coefficients is to multiply both sides by the ____________.

Correct Answer: denominator

Question 8:

The reciprocal of 2/3 is ____________.

Correct Answer: 3/2

Question 9:

An equation has an ____________ sign.

Correct Answer: equal

Question 10:

The letter that represents an unknown number is called a ____________.

Correct Answer: variable

Educational Standards

6.A.3.2:Use number sense and properties of operations and equality to model and solve mathematical problems involving equations in the form x + p = q and px = q, where p and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution. 6.N.4.3:Multiply and divide fractions and decimals using efficient and generalizable procedures. 6.A.2.1:Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to model and solve mathematical problems.

Teaching Materials

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